<?xml version="1.0" encoding="ascii"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
          "DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
  <title>equivalence</title>
  <link rel="stylesheet" href="epydoc.css" type="text/css" />
  <script type="text/javascript" src="epydoc.js"></script>
</head>

<body bgcolor="white" text="black" link="blue" vlink="#204080"
      alink="#204080">
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
       bgcolor="#a0c0ff" cellspacing="0">
  <tr valign="middle">
  <!-- Home link -->
      <th bgcolor="#70b0f0" class="navbar-select"
          >&nbsp;&nbsp;&nbsp;Home&nbsp;&nbsp;&nbsp;</th>

  <!-- Tree link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="module-tree.html">Trees</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Index link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="identifier-index.html">Indices</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Help link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="help.html">Help</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Project homepage -->
      <th class="navbar" align="right" width="100%">
        <table border="0" cellpadding="0" cellspacing="0">
          <tr><th class="navbar" align="center"
            >equivalence</th>
          </tr></table></th>
  </tr>
</table>
<table width="100%" cellpadding="0" cellspacing="0">
  <tr valign="top">
    <td width="100%">
      <span class="breadcrumbs">
        Module&nbsp;equivalence
      </span>
    </td>
    <td>
      <table cellpadding="0" cellspacing="0">
        <!-- hide/show private -->
        <tr><td align="right"><span class="options">[<a href="javascript:void(0);" class="privatelink"
    onclick="toggle_private();">hide&nbsp;private</a>]</span></td></tr>
        <tr><td align="right"><span class="options"
            >[<a href="frames.html" target="_top">frames</a
            >]&nbsp;|&nbsp;<a href="equivalence-pysrc.html"
            target="_top">no&nbsp;frames</a>]</span></td></tr>
      </table>
    </td>
  </tr>
</table>
<h1 class="epydoc">Source Code for <a href="equivalence-module.html">Module equivalence</a></h1>
<pre class="py-src">
<a name="L1"></a><tt class="py-lineno">  1</tt>  <tt class="py-line"><tt class="py-comment">#todo: docstrings, comments</tt> </tt>
<a name="L2"></a><tt class="py-lineno">  2</tt>  <tt class="py-line"><tt class="py-comment"></tt> </tt>
<a name="L3"></a><tt class="py-lineno">  3</tt>  <tt class="py-line"><tt class="py-name">__all__</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-string">'Equivalence'</tt><tt class="py-op">]</tt> </tt>
<a name="L4"></a><tt class="py-lineno">  4</tt>  <tt class="py-line"><tt class="py-name">__docformat__</tt> <tt class="py-op">=</tt> <tt class="py-string">"restructuredtext en"</tt> </tt>
<a name="L5"></a><tt class="py-lineno">  5</tt>  <tt class="py-line"><tt id="link-0" class="py-name" targets="Variable equivalence.__author__=equivalence-module.html#__author__"><a title="equivalence.__author__" class="py-name" href="#" onclick="return doclink('link-0', '__author__', 'link-0');">__author__</a></tt> <tt class="py-op">=</tt> <tt class="py-string">'George Sakkis &lt;george.sakkis AT gmail DOT com&gt;'</tt> </tt>
<a name="L6"></a><tt class="py-lineno">  6</tt>  <tt class="py-line"> </tt>
<a name="L7"></a><tt class="py-lineno">  7</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt class="py-name">collections</tt> <tt class="py-keyword">import</tt> <tt class="py-name">defaultdict</tt> </tt>
<a name="L8"></a><tt class="py-lineno">  8</tt>  <tt class="py-line"> </tt>
<a name="L9"></a><tt class="py-lineno">  9</tt>  <tt class="py-line"> </tt>
<a name="Equivalence"></a><div id="Equivalence-def"><a name="L10"></a><tt class="py-lineno"> 10</tt> <a class="py-toggle" href="#" id="Equivalence-toggle" onclick="return toggle('Equivalence');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="equivalence.Equivalence-class.html">Equivalence</a><tt class="py-op">(</tt><tt class="py-base-class">object</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Equivalence-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="Equivalence-expanded"><a name="L11"></a><tt class="py-lineno"> 11</tt>  <tt class="py-line">    <tt class="py-docstring">'''Representation of a general equivalence relation.</tt> </tt>
<a name="L12"></a><tt class="py-lineno"> 12</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L13"></a><tt class="py-lineno"> 13</tt>  <tt class="py-line"><tt class="py-docstring">    An `Equivalence` instance can be used to maintain a partition of objects</tt> </tt>
<a name="L14"></a><tt class="py-lineno"> 14</tt>  <tt class="py-line"><tt class="py-docstring">    into equivalence sets. Two objects ``x`` and ``y`` are considered</tt> </tt>
<a name="L15"></a><tt class="py-lineno"> 15</tt>  <tt class="py-line"><tt class="py-docstring">    equivalent either implicitly through a key function or explicitly. For the</tt> </tt>
<a name="L16"></a><tt class="py-lineno"> 16</tt>  <tt class="py-line"><tt class="py-docstring">    implicit case, ``x`` and ``y`` are equivalent if ``key(x) == key(y)`` for</tt> </tt>
<a name="L17"></a><tt class="py-lineno"> 17</tt>  <tt class="py-line"><tt class="py-docstring">    some provided function ``key`` (by default the identity function ``lambda x:x``).</tt> </tt>
<a name="L18"></a><tt class="py-lineno"> 18</tt>  <tt class="py-line"><tt class="py-docstring">    For the explicit case, ``x`` and ``y`` are considered equivalent after a call</tt> </tt>
<a name="L19"></a><tt class="py-lineno"> 19</tt>  <tt class="py-line"><tt class="py-docstring">    to `merge(x,y)`, regardless of their keys.</tt> </tt>
<a name="L20"></a><tt class="py-lineno"> 20</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L21"></a><tt class="py-lineno"> 21</tt>  <tt class="py-line"><tt class="py-docstring">    This class makes sure that the equivalence properties (reflexivity, symmetry,</tt> </tt>
<a name="L22"></a><tt class="py-lineno"> 22</tt>  <tt class="py-line"><tt class="py-docstring">    transitivity) are maintained, provided that ``key(x)`` remains fixed for a</tt> </tt>
<a name="L23"></a><tt class="py-lineno"> 23</tt>  <tt class="py-line"><tt class="py-docstring">    given object ``x`` (i.e. ``key`` is deterministic and does not depend on</tt> </tt>
<a name="L24"></a><tt class="py-lineno"> 24</tt>  <tt class="py-line"><tt class="py-docstring">    mutable state of ``x``).</tt> </tt>
<a name="L25"></a><tt class="py-lineno"> 25</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="L26"></a><tt class="py-lineno"> 26</tt>  <tt class="py-line"> </tt>
<a name="Equivalence.__init__"></a><div id="Equivalence.__init__-def"><a name="L27"></a><tt class="py-lineno"> 27</tt> <a class="py-toggle" href="#" id="Equivalence.__init__-toggle" onclick="return toggle('Equivalence.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="equivalence.Equivalence-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">key</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Equivalence.__init__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Equivalence.__init__-expanded"><a name="L28"></a><tt class="py-lineno"> 28</tt>  <tt class="py-line">        <tt class="py-docstring">'''Initialize a new equivalence relation.</tt> </tt>
<a name="L29"></a><tt class="py-lineno"> 29</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L30"></a><tt class="py-lineno"> 30</tt>  <tt class="py-line"><tt class="py-docstring">        :param key: A callable that takes a single argument and returns its</tt> </tt>
<a name="L31"></a><tt class="py-lineno"> 31</tt>  <tt class="py-line"><tt class="py-docstring">            equivalence key (default: identity function).</tt> </tt>
<a name="L32"></a><tt class="py-lineno"> 32</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L33"></a><tt class="py-lineno"> 33</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_keyfunc</tt> <tt class="py-op">=</tt> <tt class="py-name">key</tt> </tt>
<a name="L34"></a><tt class="py-lineno"> 34</tt>  <tt class="py-line">        <tt class="py-comment"># maps a member's key to its partition's key</tt> </tt>
<a name="L35"></a><tt class="py-lineno"> 35</tt>  <tt class="py-line"><tt class="py-comment"></tt>        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_key2pkey</tt> <tt class="py-op">=</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt> </tt>
<a name="L36"></a><tt class="py-lineno"> 36</tt>  <tt class="py-line">        <tt class="py-comment"># invert mapping of self._key2pkey:</tt> </tt>
<a name="L37"></a><tt class="py-lineno"> 37</tt>  <tt class="py-line"><tt class="py-comment"></tt>        <tt class="py-comment"># maps a partition key to the set of its partition members' keys</tt> </tt>
<a name="L38"></a><tt class="py-lineno"> 38</tt>  <tt class="py-line"><tt class="py-comment"></tt>        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2keys</tt> <tt class="py-op">=</tt> <tt class="py-name">defaultdict</tt><tt class="py-op">(</tt><tt class="py-name">set</tt><tt class="py-op">)</tt> </tt>
<a name="L39"></a><tt class="py-lineno"> 39</tt>  <tt class="py-line">        <tt class="py-comment"># maps a partition key to the set of its members</tt> </tt>
<a name="L40"></a><tt class="py-lineno"> 40</tt>  <tt class="py-line"><tt class="py-comment"></tt>        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2members</tt> <tt class="py-op">=</tt> <tt class="py-name">defaultdict</tt><tt class="py-op">(</tt><tt class="py-name">set</tt><tt class="py-op">)</tt> </tt>
</div><a name="L41"></a><tt class="py-lineno"> 41</tt>  <tt class="py-line"> </tt>
<a name="Equivalence.update"></a><div id="Equivalence.update-def"><a name="L42"></a><tt class="py-lineno"> 42</tt> <a class="py-toggle" href="#" id="Equivalence.update-toggle" onclick="return toggle('Equivalence.update');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="equivalence.Equivalence-class.html#update">update</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-param">objects</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Equivalence.update-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Equivalence.update-expanded"><a name="L43"></a><tt class="py-lineno"> 43</tt>  <tt class="py-line">        <tt class="py-docstring">'''Update this equivalence with the given objects.'''</tt> </tt>
<a name="L44"></a><tt class="py-lineno"> 44</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">obj</tt> <tt class="py-keyword">in</tt> <tt class="py-name">objects</tt><tt class="py-op">:</tt> </tt>
<a name="L45"></a><tt class="py-lineno"> 45</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2members</tt><tt class="py-op">[</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-1" class="py-name" targets="Method equivalence.Equivalence.partition_key()=equivalence.Equivalence-class.html#partition_key"><a title="equivalence.Equivalence.partition_key" class="py-name" href="#" onclick="return doclink('link-1', 'partition_key', 'link-1');">partition_key</a></tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">add</tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt> </tt>
</div><a name="L46"></a><tt class="py-lineno"> 46</tt>  <tt class="py-line"> </tt>
<a name="Equivalence.merge"></a><div id="Equivalence.merge-def"><a name="L47"></a><tt class="py-lineno"> 47</tt> <a class="py-toggle" href="#" id="Equivalence.merge-toggle" onclick="return toggle('Equivalence.merge');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="equivalence.Equivalence-class.html#merge">merge</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-param">objects</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Equivalence.merge-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Equivalence.merge-expanded"><a name="L48"></a><tt class="py-lineno"> 48</tt>  <tt class="py-line">        <tt class="py-docstring">'''Merge all the given objects into the same equivalence set.'''</tt> </tt>
<a name="L49"></a><tt class="py-lineno"> 49</tt>  <tt class="py-line">        <tt class="py-name">objects</tt> <tt class="py-op">=</tt> <tt class="py-name">iter</tt><tt class="py-op">(</tt><tt class="py-name">objects</tt><tt class="py-op">)</tt> </tt>
<a name="L50"></a><tt class="py-lineno"> 50</tt>  <tt class="py-line">        <tt class="py-keyword">try</tt><tt class="py-op">:</tt> <tt class="py-name">obj</tt> <tt class="py-op">=</tt> <tt class="py-name">objects</tt><tt class="py-op">.</tt><tt class="py-name">next</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L51"></a><tt class="py-lineno"> 51</tt>  <tt class="py-line">        <tt class="py-keyword">except</tt> <tt class="py-name">StopIteration</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> </tt>
<a name="L52"></a><tt class="py-lineno"> 52</tt>  <tt class="py-line">        <tt class="py-name">new_pkey</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-2" class="py-name"><a title="equivalence.Equivalence.partition_key" class="py-name" href="#" onclick="return doclink('link-2', 'partition_key', 'link-1');">partition_key</a></tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt> </tt>
<a name="L53"></a><tt class="py-lineno"> 53</tt>  <tt class="py-line">        <tt class="py-name">partition_members</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2members</tt><tt class="py-op">[</tt><tt class="py-name">new_pkey</tt><tt class="py-op">]</tt> </tt>
<a name="L54"></a><tt class="py-lineno"> 54</tt>  <tt class="py-line">        <tt class="py-name">partition_members</tt><tt class="py-op">.</tt><tt class="py-name">add</tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt> </tt>
<a name="L55"></a><tt class="py-lineno"> 55</tt>  <tt class="py-line">        <tt class="py-name">key2pkey</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_key2pkey</tt> </tt>
<a name="L56"></a><tt class="py-lineno"> 56</tt>  <tt class="py-line">        <tt class="py-name">partition_keys</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2keys</tt><tt class="py-op">[</tt><tt class="py-name">new_pkey</tt><tt class="py-op">]</tt> </tt>
<a name="L57"></a><tt class="py-lineno"> 57</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">obj</tt> <tt class="py-keyword">in</tt> <tt class="py-name">objects</tt><tt class="py-op">:</tt> </tt>
<a name="L58"></a><tt class="py-lineno"> 58</tt>  <tt class="py-line">            <tt class="py-name">partition_members</tt><tt class="py-op">.</tt><tt class="py-name">add</tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt> </tt>
<a name="L59"></a><tt class="py-lineno"> 59</tt>  <tt class="py-line">            <tt class="py-name">old_pkey</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-3" class="py-name"><a title="equivalence.Equivalence.partition_key" class="py-name" href="#" onclick="return doclink('link-3', 'partition_key', 'link-1');">partition_key</a></tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt> </tt>
<a name="L60"></a><tt class="py-lineno"> 60</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">old_pkey</tt> <tt class="py-op">!=</tt> <tt class="py-name">new_pkey</tt><tt class="py-op">:</tt> </tt>
<a name="L61"></a><tt class="py-lineno"> 61</tt>  <tt class="py-line">                <tt class="py-name">key2pkey</tt><tt class="py-op">[</tt><tt class="py-name">old_pkey</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">new_pkey</tt> </tt>
<a name="L62"></a><tt class="py-lineno"> 62</tt>  <tt class="py-line">                <tt class="py-name">partition_keys</tt><tt class="py-op">.</tt><tt class="py-name">add</tt><tt class="py-op">(</tt><tt class="py-name">old_pkey</tt><tt class="py-op">)</tt> </tt>
<a name="L63"></a><tt class="py-lineno"> 63</tt>  <tt class="py-line">                <tt class="py-keyword">for</tt> <tt class="py-name">key</tt> <tt class="py-keyword">in</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2keys</tt><tt class="py-op">.</tt><tt class="py-name">pop</tt><tt class="py-op">(</tt><tt class="py-name">old_pkey</tt><tt class="py-op">,</tt> <tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L64"></a><tt class="py-lineno"> 64</tt>  <tt class="py-line">                    <tt class="py-name">key2pkey</tt><tt class="py-op">[</tt><tt class="py-name">key</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">new_pkey</tt> </tt>
<a name="L65"></a><tt class="py-lineno"> 65</tt>  <tt class="py-line">                    <tt class="py-name">partition_keys</tt><tt class="py-op">.</tt><tt class="py-name">add</tt><tt class="py-op">(</tt><tt class="py-name">key</tt><tt class="py-op">)</tt> </tt>
<a name="L66"></a><tt class="py-lineno"> 66</tt>  <tt class="py-line">                <tt class="py-name">partition_members</tt><tt class="py-op">.</tt><tt id="link-4" class="py-name" targets="Method equivalence.Equivalence.update()=equivalence.Equivalence-class.html#update"><a title="equivalence.Equivalence.update" class="py-name" href="#" onclick="return doclink('link-4', 'update', 'link-4');">update</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2members</tt><tt class="py-op">.</tt><tt class="py-name">pop</tt><tt class="py-op">(</tt><tt class="py-name">old_pkey</tt><tt class="py-op">,</tt> <tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L67"></a><tt class="py-lineno"> 67</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">partition_keys</tt><tt class="py-op">:</tt> <tt class="py-comment"># don't need to key empty sets</tt> </tt>
<a name="L68"></a><tt class="py-lineno"> 68</tt>  <tt class="py-line">            <tt class="py-keyword">del</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2members</tt><tt class="py-op">[</tt><tt class="py-name">new_pkey</tt><tt class="py-op">]</tt> </tt>
</div><a name="L69"></a><tt class="py-lineno"> 69</tt>  <tt class="py-line"> </tt>
<a name="Equivalence.are_equivalent"></a><div id="Equivalence.are_equivalent-def"><a name="L70"></a><tt class="py-lineno"> 70</tt> <a class="py-toggle" href="#" id="Equivalence.are_equivalent-toggle" onclick="return toggle('Equivalence.are_equivalent');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="equivalence.Equivalence-class.html#are_equivalent">are_equivalent</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-param">objects</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Equivalence.are_equivalent-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Equivalence.are_equivalent-expanded"><a name="L71"></a><tt class="py-lineno"> 71</tt>  <tt class="py-line">        <tt class="py-docstring">'''Checks whether all objects are equivalent.</tt> </tt>
<a name="L72"></a><tt class="py-lineno"> 72</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L73"></a><tt class="py-lineno"> 73</tt>  <tt class="py-line"><tt class="py-docstring">        An object doesn't have to be inserted first (through `update` or `merge`)</tt> </tt>
<a name="L74"></a><tt class="py-lineno"> 74</tt>  <tt class="py-line"><tt class="py-docstring">        in order to appear as an argument. In this case, its ``key`` is used to</tt> </tt>
<a name="L75"></a><tt class="py-lineno"> 75</tt>  <tt class="py-line"><tt class="py-docstring">        determine the partition it would belong if it was inserted.</tt> </tt>
<a name="L76"></a><tt class="py-lineno"> 76</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L77"></a><tt class="py-lineno"> 77</tt>  <tt class="py-line"><tt class="py-docstring">        :rtype: bool</tt> </tt>
<a name="L78"></a><tt class="py-lineno"> 78</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L79"></a><tt class="py-lineno"> 79</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">objects</tt><tt class="py-op">:</tt> </tt>
<a name="L80"></a><tt class="py-lineno"> 80</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'No objects given'</tt><tt class="py-op">)</tt> </tt>
<a name="L81"></a><tt class="py-lineno"> 81</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">set</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-5" class="py-name"><a title="equivalence.Equivalence.partition_key" class="py-name" href="#" onclick="return doclink('link-5', 'partition_key', 'link-1');">partition_key</a></tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">obj</tt> <tt class="py-keyword">in</tt> <tt class="py-name">objects</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt> </tt>
</div><a name="L82"></a><tt class="py-lineno"> 82</tt>  <tt class="py-line"> </tt>
<a name="Equivalence.partitions"></a><div id="Equivalence.partitions-def"><a name="L83"></a><tt class="py-lineno"> 83</tt> <a class="py-toggle" href="#" id="Equivalence.partitions-toggle" onclick="return toggle('Equivalence.partitions');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="equivalence.Equivalence-class.html#partitions">partitions</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">objects</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Equivalence.partitions-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Equivalence.partitions-expanded"><a name="L84"></a><tt class="py-lineno"> 84</tt>  <tt class="py-line">        <tt class="py-docstring">'''Returns the partitioning of `objects` into equivalence groups.</tt> </tt>
<a name="L85"></a><tt class="py-lineno"> 85</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L86"></a><tt class="py-lineno"> 86</tt>  <tt class="py-line"><tt class="py-docstring">        :type objects: Iterable or None</tt> </tt>
<a name="L87"></a><tt class="py-lineno"> 87</tt>  <tt class="py-line"><tt class="py-docstring">        :param objects: If not None, it must be an iterable of objects to be</tt> </tt>
<a name="L88"></a><tt class="py-lineno"> 88</tt>  <tt class="py-line"><tt class="py-docstring">            partitioned. Otherwise, it defaults to the set of objects already</tt> </tt>
<a name="L89"></a><tt class="py-lineno"> 89</tt>  <tt class="py-line"><tt class="py-docstring">            inserted in the equivalence (through `update` and `merge`).</tt> </tt>
<a name="L90"></a><tt class="py-lineno"> 90</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L91"></a><tt class="py-lineno"> 91</tt>  <tt class="py-line"><tt class="py-docstring">        :returns: A list of partitions, each partition being a list of objects.</tt> </tt>
<a name="L92"></a><tt class="py-lineno"> 92</tt>  <tt class="py-line"><tt class="py-docstring">        :rtype: list of lists</tt> </tt>
<a name="L93"></a><tt class="py-lineno"> 93</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L94"></a><tt class="py-lineno"> 94</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">objects</tt><tt class="py-op">:</tt> </tt>
<a name="L95"></a><tt class="py-lineno"> 95</tt>  <tt class="py-line">            <tt class="py-name">objects</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">obj</tt> <tt class="py-keyword">for</tt> <tt class="py-name">members</tt> <tt class="py-keyword">in</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2members</tt><tt class="py-op">.</tt><tt class="py-name">itervalues</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L96"></a><tt class="py-lineno"> 96</tt>  <tt class="py-line">                       <tt class="py-keyword">for</tt> <tt class="py-name">obj</tt> <tt class="py-keyword">in</tt> <tt class="py-name">members</tt><tt class="py-op">)</tt> </tt>
<a name="L97"></a><tt class="py-lineno"> 97</tt>  <tt class="py-line">        <tt class="py-name">key2partition</tt> <tt class="py-op">=</tt> <tt class="py-name">defaultdict</tt><tt class="py-op">(</tt><tt class="py-name">list</tt><tt class="py-op">)</tt> </tt>
<a name="L98"></a><tt class="py-lineno"> 98</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">obj</tt> <tt class="py-keyword">in</tt> <tt class="py-name">objects</tt><tt class="py-op">:</tt> </tt>
<a name="L99"></a><tt class="py-lineno"> 99</tt>  <tt class="py-line">            <tt class="py-name">key2partition</tt><tt class="py-op">[</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-6" class="py-name"><a title="equivalence.Equivalence.partition_key" class="py-name" href="#" onclick="return doclink('link-6', 'partition_key', 'link-1');">partition_key</a></tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">append</tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt> </tt>
<a name="L100"></a><tt class="py-lineno">100</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">key2partition</tt><tt class="py-op">.</tt><tt class="py-name">values</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L101"></a><tt class="py-lineno">101</tt>  <tt class="py-line"> </tt>
<a name="Equivalence.partition"></a><div id="Equivalence.partition-def"><a name="L102"></a><tt class="py-lineno">102</tt> <a class="py-toggle" href="#" id="Equivalence.partition-toggle" onclick="return toggle('Equivalence.partition');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="equivalence.Equivalence-class.html#partition">partition</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">obj</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Equivalence.partition-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Equivalence.partition-expanded"><a name="L103"></a><tt class="py-lineno">103</tt>  <tt class="py-line">        <tt class="py-docstring">'''Return the set of objects in the equivalence that are equivalent to</tt> </tt>
<a name="L104"></a><tt class="py-lineno">104</tt>  <tt class="py-line"><tt class="py-docstring">        `obj`.</tt> </tt>
<a name="L105"></a><tt class="py-lineno">105</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L106"></a><tt class="py-lineno">106</tt>  <tt class="py-line"><tt class="py-docstring">        :rtype: set</tt> </tt>
<a name="L107"></a><tt class="py-lineno">107</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L108"></a><tt class="py-lineno">108</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_pkey2members</tt><tt class="py-op">.</tt><tt class="py-name">get</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-7" class="py-name"><a title="equivalence.Equivalence.partition_key" class="py-name" href="#" onclick="return doclink('link-7', 'partition_key', 'link-1');">partition_key</a></tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-name">set</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L109"></a><tt class="py-lineno">109</tt>  <tt class="py-line"> </tt>
<a name="Equivalence.partition_key"></a><div id="Equivalence.partition_key-def"><a name="L110"></a><tt class="py-lineno">110</tt> <a class="py-toggle" href="#" id="Equivalence.partition_key-toggle" onclick="return toggle('Equivalence.partition_key');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="equivalence.Equivalence-class.html#partition_key">partition_key</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">obj</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Equivalence.partition_key-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Equivalence.partition_key-expanded"><a name="L111"></a><tt class="py-lineno">111</tt>  <tt class="py-line">        <tt class="py-docstring">'''Return the key of the equivalence partition `obj` belongs to.'''</tt> </tt>
<a name="L112"></a><tt class="py-lineno">112</tt>  <tt class="py-line">        <tt class="py-name">key</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_keyfunc</tt><tt class="py-op">(</tt><tt class="py-name">obj</tt><tt class="py-op">)</tt> <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_keyfunc</tt> <tt class="py-keyword">else</tt> <tt class="py-name">obj</tt> </tt>
<a name="L113"></a><tt class="py-lineno">113</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_key2pkey</tt><tt class="py-op">.</tt><tt class="py-name">get</tt><tt class="py-op">(</tt><tt class="py-name">key</tt><tt class="py-op">,</tt><tt class="py-name">key</tt><tt class="py-op">)</tt> </tt>
</div></div><a name="L114"></a><tt class="py-lineno">114</tt>  <tt class="py-line"> </tt><script type="text/javascript">
<!--
expandto(location.href);
// -->
</script>
</pre>
<br />
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
       bgcolor="#a0c0ff" cellspacing="0">
  <tr valign="middle">
  <!-- Home link -->
      <th bgcolor="#70b0f0" class="navbar-select"
          >&nbsp;&nbsp;&nbsp;Home&nbsp;&nbsp;&nbsp;</th>

  <!-- Tree link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="module-tree.html">Trees</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Index link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="identifier-index.html">Indices</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Help link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="help.html">Help</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Project homepage -->
      <th class="navbar" align="right" width="100%">
        <table border="0" cellpadding="0" cellspacing="0">
          <tr><th class="navbar" align="center"
            >equivalence</th>
          </tr></table></th>
  </tr>
</table>
<table border="0" cellpadding="0" cellspacing="0" width="100%%">
  <tr>
    <td align="left" class="footer">
    Generated by Epydoc 3.0beta1 on Sun Jun 01 10:18:20 2008
    </td>
    <td align="right" class="footer">
      <a href="http://epydoc.sourceforge.net">http://epydoc.sourceforge.net</a>
    </td>
  </tr>
</table>

<script type="text/javascript">
  <!--
  // Private objects are initially displayed (because if
  // javascript is turned off then we want them to be
  // visible); but by default, we want to hide them.  So hide
  // them unless we have a cookie that says to show them.
  checkCookie()
  // -->
</script>
  
</body>
</html>
